1D Landau-Ginzburg Superpotential of Big Quantum Cohomology of ℂℙ²
Using the inverse period map of the Gauss-Manin connection associated with *(ℂℙ²) and the Dubrovin construction of Landau-Ginzburg superpotential for Dubrovin-Frobenius manifolds, we construct a one-dimensional Landau-Ginzburg superpotential for the quantum cohomology of ℂℙ². In the case of small qu...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2025 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2025
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/213177 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 1D Landau-Ginzburg Superpotential of Big Quantum Cohomology of ℂℙ². Guilherme F. Almeida. SIGMA 21 (2025), 038, 65 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862739786460037120 |
|---|---|
| author | Almeida, Guilherme F. |
| author_facet | Almeida, Guilherme F. |
| citation_txt | 1D Landau-Ginzburg Superpotential of Big Quantum Cohomology of ℂℙ². Guilherme F. Almeida. SIGMA 21 (2025), 038, 65 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Using the inverse period map of the Gauss-Manin connection associated with *(ℂℙ²) and the Dubrovin construction of Landau-Ginzburg superpotential for Dubrovin-Frobenius manifolds, we construct a one-dimensional Landau-Ginzburg superpotential for the quantum cohomology of ℂℙ². In the case of small quantum cohomology, the Landau-Ginzburg superpotential is expressed in terms of the cubic root of the -invariant function. For big quantum cohomology, the one-dimensional Landau-Ginzburg superpotential is given by Taylor series expansions whose coefficients are expressed in terms of quasi-modular forms. Furthermore, we express the Landau-Ginzburg superpotential for both small and big quantum cohomology of *(ℂℙ²) in closed form as the composition of the Weierstrass ℘-function and the universal coverings of ℂ∖(ℤ⊕eπⁱᐟ³ℤ) and ℂ∖(ℤ⊕ℤ), respectively.
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| first_indexed | 2026-03-21T18:41:26Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-213177 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T18:41:26Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Almeida, Guilherme F. 2026-02-16T16:33:40Z 2025 1D Landau-Ginzburg Superpotential of Big Quantum Cohomology of ℂℙ². Guilherme F. Almeida. SIGMA 21 (2025), 038, 65 pages 1815-0659 2020 Mathematics Subject Classification: 53D45 arXiv:2402.09574 https://nasplib.isofts.kiev.ua/handle/123456789/213177 https://doi.org/10.3842/SIGMA.2025.038 Using the inverse period map of the Gauss-Manin connection associated with *(ℂℙ²) and the Dubrovin construction of Landau-Ginzburg superpotential for Dubrovin-Frobenius manifolds, we construct a one-dimensional Landau-Ginzburg superpotential for the quantum cohomology of ℂℙ². In the case of small quantum cohomology, the Landau-Ginzburg superpotential is expressed in terms of the cubic root of the -invariant function. For big quantum cohomology, the one-dimensional Landau-Ginzburg superpotential is given by Taylor series expansions whose coefficients are expressed in terms of quasi-modular forms. Furthermore, we express the Landau-Ginzburg superpotential for both small and big quantum cohomology of *(ℂℙ²) in closed form as the composition of the Weierstrass ℘-function and the universal coverings of ℂ∖(ℤ⊕eπⁱᐟ³ℤ) and ℂ∖(ℤ⊕ℤ), respectively. I am grateful to Professor Hertling for his remarkable advice, guidance, and for proofreading this manuscript. Furthermore, I would also like to thank Professors Doran and Milanov for helpful discussions. I am also thankful to the anonymous referees for their valuable comments and suggestions. This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – 494849004. The work was carried out while I was at the University of Mannheim, and I now work at the Max Planck Institute of Molecular Cell Biology and Genetics, Dresden. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications 1D Landau-Ginzburg Superpotential of Big Quantum Cohomology of ℂℙ² Article published earlier |
| spellingShingle | 1D Landau-Ginzburg Superpotential of Big Quantum Cohomology of ℂℙ² Almeida, Guilherme F. |
| title | 1D Landau-Ginzburg Superpotential of Big Quantum Cohomology of ℂℙ² |
| title_full | 1D Landau-Ginzburg Superpotential of Big Quantum Cohomology of ℂℙ² |
| title_fullStr | 1D Landau-Ginzburg Superpotential of Big Quantum Cohomology of ℂℙ² |
| title_full_unstemmed | 1D Landau-Ginzburg Superpotential of Big Quantum Cohomology of ℂℙ² |
| title_short | 1D Landau-Ginzburg Superpotential of Big Quantum Cohomology of ℂℙ² |
| title_sort | 1d landau-ginzburg superpotential of big quantum cohomology of ℂℙ² |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/213177 |
| work_keys_str_mv | AT almeidaguilhermef 1dlandauginzburgsuperpotentialofbigquantumcohomologyofcp2 |